Compute magnetic flux density: a flux of 5.5 µWb passes through a cross-sectional area of 6 × 10^–3 m^2. What is B?

Introduction / Context:Flux density B measures how concentrated magnetic flux Φ is over an area A. It is directly used in core design, sensor calibration, and magnetic circuit analysis. Converting units carefully (microwebers to webers) and applying the B = Φ / A definition are the keys here.

Given Data / Assumptions:

• Magnetic flux Φ = 5.5 µWb = 5.5 * 10^-6 Wb.
• Cross-sectional area A = 6 * 10^-3 m^2.
• Uniform distribution of flux over the area (standard assumption for calculation).

Concept / Approach:Use the fundamental relation B = Φ / A. Then convert the resulting tesla value into microtesla (1 T = 10^6 µT) to match typical engineering magnitudes for small flux/large area scenarios.

Step-by-Step Solution:

Verification / Alternative check:Dimensional check: Φ in Wb divided by A in m^2 yields Wb/m^2, which equals tesla. Magnitude check: small flux over millimeter-scale area gives sub-millitesla values; hundreds of microtesla is reasonable.

Why Other Options Are Wrong:

• 91.7 µT: Off by a factor of 10 due to a power-of-ten slip.
• 9.7 T or 91 T: Unrealistically large; would imply extreme fields not supported by the given micro-weber flux and millimeter-scale area.

Common Pitfalls:

• Mistaking µWb for Wb, causing six orders of magnitude error.
• Forgetting to divide by the area in square meters.

Final Answer:917 µT